Table of Contents
Preface v
Chapter 1 Linear Spaces and Linear Mappings
11 Linear spaces 1
12 Linear mappings 6
13 Subspaces 11
14 Linear partitions 20
15 Supplements 24
Chapter 2 Properties of Linear Mappings
21 Linear invertibility 29
22 Cancellability and factorization 34
Chapter 3 Linear Products and Coproducts
31 Linear products 39
32 Linear coproducts 44
33 Decompositions 49
Chapter 4 Families in Linear Spaces
41 Linear combination 57
42 Linear' independence 60
43 Linear independence, spanning, bases 65
Chapter 5 Finite Dimension
51 Matrices 73
52 Finite-dimensional spaces 77
53 Finite dimension and linear mappings 83
54 Finite- and infinite-dimensional spaces 90
Chapter 6 Duality
61 Dual spaces and transposes 93
62 Annihilators 97
63 Higher-order dual spaces and transposes 106
64 Biortliogonal families 110
Chapter 7 Duality and Finite Dimension
71 Duality for finite-dimensional spaces 113
72 Dual bases and matrices 117
73 The trace form 121
74 The canonical identifications 127
Indexes
Index of terms 129
Index of symbols 131
